A black hole merger (or BH merger), the joining of two black holes, becomes likely when the orbit of a black hole binary becomes sufficiently small that gravitational waves sap energy from the orbit, causing it to appreciably decay. The result of the merger is a black hole with most of the mass of the sum of the two. When the two merge, a gravitational wave event may result, and if they are stellar mass black holes, the ground gravitational-wave detectors, LIGO and Virgo can detect them within a certain radius. Five of the first six GW detections are ascribed to black hole mergers, based upon the determined mass of the merging objects and how close together they must be to produce the highest observed wave frequency (to be close together yet orbiting, they must be compact and a black hole is the most compact form of mass).
Some sort of help is needed to tighten the orbit to point where GWs bring about the merger. For binary SMBHs, figuring out the source of this "help" constitutes the final parsec problem. Such a problem also exists for stellar mass black holes, and what sort of mechanism can bring sufficiently close within the age of the universe is an area of current theory and analysis. One possibility is a third object in the system (i.e., a triple system), influencing the BH orbit. A likely mechanism is the Kozai mechanism, increasing the eccentricity of the coorbiting black holes to the point where at the periapsis, the removal of energy by gravitational waves is sufficiently significant to decay the orbit. Sufficient decay is still likely to require gigayears.
To become such a system, the earlier binary star must have included massive stars, easily sufficient to undergo giant stages, and even with the influence of a third object, they must have started out orbiting fairly close to each other. This makes it likely that they interacted (close binary or contact binary), even to the extent of one orbiting within the other's envelope during some stages of the system's life. The resulting drag would also harden the orbit. Cases have been observed of giant stars that may have black hole companions.
LISA aims detect black hole binaries while the black holes are further apart, still in larger orbits, producing a lower frequency gravitational wave.